x^96-1 eching

$${ x }^{ 96 } -1$$

Omil

$$\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right)\left(x^{2}-x+1\right)\left(x^{2}+x+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)\left(x^{16}+1\right)\left(x^{60}-x^{58}+x^{54}-x^{52}+x^{48}-x^{46}+x^{42}-x^{40}+x^{36}-x^{34}+x^{30}-x^{26}+x^{24}-x^{20}+x^{18}-x^{14}+x^{12}-x^{8}+x^{6}-x^{2}+1\right)$$

Yechim qadamlari

x^{96}-1 ni \left(x^{48}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{48}-1\right)\left(x^{48}+1\right)$$

Hisoblang: x^{48}-1. x^{48}-1 ni \left(x^{24}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{24}-1\right)\left(x^{24}+1\right)$$

Hisoblang: x^{24}-1. x^{24}-1 ni \left(x^{12}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{12}-1\right)\left(x^{12}+1\right)$$

Hisoblang: x^{12}-1. x^{12}-1 ni \left(x^{6}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{6}-1\right)\left(x^{6}+1\right)$$

Hisoblang: x^{6}-1. x^{6}-1 ni \left(x^{3}\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{3}-1\right)\left(x^{3}+1\right)$$

Hisoblang: x^{3}-1. x^{3}-1 ni x^{3}-1^{3} sifatida qaytadan yozish. Kublarning farqini ushbu formula bilan hisoblash mumkin: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(x-1\right)\left(x^{2}+x+1\right)$$

Hisoblang: x^{3}+1. x^{3}+1 ni x^{3}+1^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x+1\right)\left(x^{2}-x+1\right)$$

Hisoblang: x^{6}+1. x^{6}+1 ni \left(x^{2}\right)^{3}+1^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x^{2}+1\right)\left(x^{4}-x^{2}+1\right)$$

Hisoblang: x^{12}+1. x^{12}+1 ni \left(x^{4}\right)^{3}+1^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x^{4}+1\right)\left(x^{8}-x^{4}+1\right)$$

Hisoblang: x^{24}+1. x^{24}+1 ni \left(x^{8}\right)^{3}+1^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x^{8}+1\right)\left(x^{16}-x^{8}+1\right)$$

Hisoblang: x^{48}+1. x^{48}+1 ni \left(x^{16}\right)^{3}+1^{3} sifatida qaytadan yozish. Kublar yigʻindisini ushbu formula bilan hisoblash mumkin: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x^{16}+1\right)\left(x^{32}-x^{16}+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing. Quyidagi koʻphadlar faktorlanmagan, ularda hech qanday ratsional ildizlar topilmadi: x^{2}-x+1,x^{2}+x+1,x^{4}-x^{2}+1,x^{2}+1,x^{8}-x^{4}+1,x^{4}+1,x^{16}-x^{8}+1,x^{8}+1,x^{32}-x^{16}+1,x^{16}+1.

$$\left(x-1\right)\left(x^{2}-x+1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{4}-x^{2}+1\right)\left(x^{2}+1\right)\left(x^{8}-x^{4}+1\right)\left(x^{4}+1\right)\left(x^{16}-x^{8}+1\right)\left(x^{8}+1\right)\left(x^{32}-x^{16}+1\right)\left(x^{16}+1\right)$$

Baholash

$$x^{96}-1$$